Quaternionic representation of snub 24-cell and its dual polytope derived from \(E_8\) root system. (Q624359)

The authors study the symmetry group of the semiregular \(4D\) polytope snub \(24\)-cell. In particular, they construct its \(96\) vertices in terms of quaternions and the root system of \(E_8\) using two sets of quaternionic representations of the \(D_4\) roots as well as its weights of three \(8\)-dimensional representations. They introduce the quaternionic root system of \(H_4\) decomposed in terms of its conjugacy classes and construct the maximal subgroup \((W(D_4)/C_2):S_3\) of \(W(H_4)\).